A body has to travel 120km distance. It travels first 30km with uniform speed 30km/hr. Its average speed is 60 km/hr. What should be its speed in next 90 km distance?

Explanation

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the given information
- Total distance to be traveled = 120 km
- Distance traveled in the first part = 30 km
- Speed during the first part = 30 km/hr
- Average speed for the entire journey = 60 km/hr

### Step 2: Calculate the total time for the journey
Using the formula for average speed:
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \]
We can rearrange this to find the total time:
\[ \text{Total Time} = \frac{\text{Total Distance}}{\text{Average Speed}} = \frac{120 \text{ km}}{60 \text{ km/hr}} = 2 \text{ hours} \]

### Step 3: Calculate the time taken for the first part of the journey
Using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
For the first part:
\[ T_1 = \frac{30 \text{ km}}{30 \text{ km/hr}} = 1 \text{ hour} \]

### Step 4: Calculate the time remaining for the second part of the journey
Since the total time for the journey is 2 hours and the time taken for the first part is 1 hour:
\[ T_2 = \text{Total Time} - T_1 = 2 \text{ hours} - 1 \text{ hour} = 1 \text{ hour} \]

### Step 5: Calculate the speed required for the second part of the journey
Using the formula for speed:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
For the second part:
\[ V_2 = \frac{90 \text{ km}}{T_2} = \frac{90 \text{ km}}{1 \text{ hour}} = 90 \text{ km/hr} \]

### Final Answer
The speed required for the next 90 km distance is **90 km/hr**.

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